The use of directional antennas in wireless ad hoc networks can signiﬁcantly improve global performance due to a high spatial channel reuse. Nevertheless, its introduction poses new location dependent problems related to the MAC protocol. In this paper, the Balanced Incomplete Block Design theory has been exploited to develop a new MAC protocol for wireless ad hoc networks using directional antennas. It is a time slotted protocol, which is highly scalable. Moreover, it can provide a high number of concurrent communications, depending on the number of directional antennas mounted on each node, great fairness in bandwidth sharing and signiﬁcant energy saving. In particular, energy saving provided by our scheme is consistently higher compared to those of usual directional MAC protocols for the following reasons. Firstly, control packets are sent only over fairly selected beams rather than over all the available ones. Secondly, our protocol provides a ﬁltering, i.e. a fair selection, of the nodes that can try the access to the medium in each time slot. Simulation results validate the advantages of our protocol by proving high spatial reuse, great fairness and signiﬁcant energy saving and by showing that it improves the overall system performance.